Sci-Fi Movies for the Unsuspecting Non-Sci-Fi Fan

After seeing a few exceptional trailers (1, 2, 3) for Lars von Trier's Melancholia, starring Kirsten Dunst, I started to think about all the sci-fi movies that mask themselves as a different genre altogether.
One of my favorite movies of all time is Repo Man. With taglines like "Let's do some crimes!" and "...It's 4 A.M., do you know where your car is?", it's hard for most people to even imagine that it's a sci-fi movie. Yet, one of my favorite alien theories came from this film - see video below to hear Miller's theory on time travel and aliens:

Another one of these unsuspecting sci-fi films is Dude, Where's My Car? After seeing countless commercials portraying it as a stoner comedy, who would've known that it was actually a pretty decent sci-fi movie? I didn't go see it in the movie theater, and was NOT the one who selected it as a rental, but was mind-blowingly surprised when it had more to it than mindless idiocy.

So there you go, two unsuspecting, but entertaining little sci-fi movies for you to add to your Netflix queue... because if you haven't seen them yet, you need to. Well, at least Repo Man. ;)

Are there any other English language films that I should add to this list? Let me know in the comments... I'm genuinely interested.